If your application is for developers, chances are good that it could benefit from integration with source control.
Even non-developer applications, such as document editors, could potentially benefit from version-control features, and Git’s model works very well for many different scenarios.

If you need to integrate Git with your application, you have essentially three choices: spawning a shell and using the Git command-line tool; Libgit2; and JGit.

Command-line Git

One option is to spawn a shell process and use the Git command-line tool to do the work.
This has the benefit of being canonical, and all of Git’s features are supported.
This also happens to be fairly easy, as most runtime environments have a relatively simple facility for invoking a process with command-line arguments.
However, this approach does have some downsides.

One is that all the output is in plain text.
This means that you’ll have to parse Git’s occasionally-changing output format to read progress and result information, which can be inefficient and error-prone.

Another is the lack of error recovery.
If a repository is corrupted somehow, or the user has a malformed configuration value, Git will simply refuse to perform many operations.

Yet another is process management.
Git requires you to maintain a shell environment on a separate process, which can add unwanted complexity.
Trying to coordinate many of these processes (especially when potentially accessing the same repository from several processes) can be quite a challenge.